Information asymmetry in games enables players with the information advantage to manipulate others' beliefs by strategically revealing information to other players. This work considers a double-sided information asymmetry in a Bayesian Stackelberg game, where the leader's realized action, sampled from the mixed strategy commitment, is hidden from the follower. In contrast, the follower holds private information about his payoff. Given asymmetric information on both sides, an important question arises: \emph{Does the leader's information advantage outweigh the follower's?} We answer this question affirmatively in this work, where we demonstrate that by adequately designing a signaling device that reveals partial information regarding the leader's realized action to the follower, the leader can achieve a higher expected utility than that without signaling. Moreover, unlike previous works on the Bayesian Stackelberg game where mathematical programming tools are utilized, we interpret the leader's commitment as a probability measure over the belief space. Such a probabilistic language greatly simplifies the analysis and allows an indirect signaling scheme, leading to a geometric characterization of the equilibrium under the proposed game model.

We investigate experiments that are designed to select a treatment arm for population deployment. Multi-armed bandit algorithms can enhance efficiency by dynamically allocating measurement effort towards higher performing arms based on observed feedback. However, such dynamics can result in brittle behavior in the face of nonstationary exogenous factors influencing arms' performance during the experiment. To counter this, we propose deconfounded Thompson sampling (DTS), a more robust variant of the prominent Thompson sampling algorithm. As observations accumulate, DTS projects the population-level performance of an arm while controlling for the context within which observed treatment decisions were made. Contexts here might capture a comprehensible source of variation, such as the country of a treated individual, or simply record the time of treatment. We provide bounds on both within-experiment and post-experiment regret of DTS, illustrating its resilience to exogenous variation and the delicate balance it strikes between exploration and exploitation. Our proofs leverage inverse propensity weights to analyze the evolution of the posterior distribution, a departure from established methods in the literature. Hinting that new understanding is indeed necessary, we show that a deconfounded variant of the popular upper confidence bound algorithm can fail completely.

Physics informed neural network (PINN) approach in Bayesian formulation is presented. We adopt the Bayesian neural network framework formulated by MacKay (Neural Computation 4 (3) (1992) 448). The posterior densities are obtained from Laplace approximation. For each model (fit), the so-called evidence is computed. It is a measure that classifies the hypothesis. The most optimal solution has the maximal value of the evidence. The Bayesian framework allows us to control the impact of the boundary contribution to the total loss. Indeed, the relative weights of loss components are fine-tuned by the Bayesian algorithm. We solve heat, wave, and Burger's equations. The obtained results are in good agreement with the exact solutions. All solutions are provided with the uncertainties computed within the Bayesian framework.

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and requires tuning parameters. Moreover, ADVI inherits the poor posterior uncertainty estimates of mean-field variational Bayes (MFVB). We introduce "deterministic ADVI" (DADVI) to address these issues. DADVI replaces the intractable MFVB objective with a fixed Monte Carlo approximation, a technique known in the stochastic optimization literature as the "sample average approximation" (SAA). By optimizing an approximate but deterministic objective, DADVI can use off-the-shelf second-order optimization, and, unlike standard mean-field ADVI, is amenable to more accurate posterior covariances via linear response (LR). In contrast to existing worst-case theory, we show that, on certain classes of common statistical problems, DADVI and the SAA can perform well with relatively few samples even in very high dimensions, though we also show that such favorable results cannot extend to variational approximations that are too expressive relative to mean-field ADVI. We show on a variety of real-world problems that DADVI reliably finds good solutions with default settings (unlike ADVI) and, together with LR covariances, is typically faster and more accurate than standard ADVI.

Offshore wind structures are subject to deterioration mechanisms throughout their operational lifetime. Even if the deterioration evolution of structural elements can be estimated through physics-based deterioration models, the uncertainties involved in the process hurdle the selection of lifecycle management decisions. In this scenario, the collection of relevant information through an efficient monitoring system enables the reduction of uncertainties, ultimately driving more optimal lifecycle decisions. However, a full monitoring instrumentation implemented on all wind turbines in a farm might become unfeasible due to practical and economical constraints. Besides, certain load monitoring systems often become defective after a few years of marine environment exposure. Addressing the aforementioned concerns, a farm-wide virtual load monitoring scheme directed by a fleet-leader wind turbine offers an attractive solution. Fetched with data retrieved from a fully-instrumented wind turbine, a model can be trained and then deployed, thus yielding load predictions of non-fully monitored wind turbines, from which only standard data remains available. In this paper, we propose a virtual load monitoring framework formulated via Bayesian neural networks (BNNs) and we provide relevant implementation details needed for the construction, training, and deployment of BNN data-based virtual monitoring models. As opposed to their deterministic counterparts, BNNs intrinsically announce the uncertainties associated with generated load predictions and allow to detect inaccurate load estimations generated for non-fully monitored wind turbines. The proposed virtual load monitoring is thoroughly tested through an experimental campaign in an operational offshore wind farm and the results demonstrate the effectiveness of BNN models for fleet-leader-based farm-wide virtual monitoring.

We propose an optimization algorithm for Variational Inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for Gaussian Variational Inference that implicitly satisfies the positive definite constraint on the variational covariance matrix. Our Exact manifold Gaussian Variational Bayes (EMGVB) provides exact but simple update rules and is straightforward to implement. Due to its black-box nature, EMGVB stands as a ready-to-use solution for VI in complex models. Over five datasets, we empirically validate our feasible approach on different statistical, econometric, and deep learning models, discussing its performance with respect to baseline methods.

Extended target tracking estimates the centroid and shape of the target in space and time. In various situations where extended target tracking is applicable, the presence of multiple targets can lead to interference, particularly when they maneuver behind one another in a sensor like a camera. Nonetheless, when dealing with multiple extended targets, there's a tendency for them to share similar shapes within a group, which can enhance their detectability. For instance, the coordinated movement of a cluster of aerial vehicles might cause radar misdetections during their convergence or divergence. Similarly, in the context of a self-driving car, lane markings might split or converge, resulting in inaccurate lane tracking detections. A well-known joint probabilistic data association coupled (JPDAC) filter can address this problem in only a single-point target tracking. A variation of JPDACF was developed by introducing a nonparametric Spatio-Temporal Joint Probabilistic Data Association Coupled Filter (ST-JPDACF) to address the problem for extended targets. Using different kernel functions, we manage the dependency of measurements in space (inside a frame) and time (between frames). Kernel functions are able to be learned using a limited number of training data. This extension can be used for tracking the shape and dynamics of nonparametric dependent extended targets in clutter when targets share measurements. The proposed algorithm was compared with other well-known supervised methods in the interfering case and achieved promising results.

A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior distributions over model parameters, a process known as prior elicitation. Expert knowledge can manifest itself in diverse formats, including information about raw data, summary statistics, or model parameters. A major challenge for existing elicitation methods is how to effectively utilize all of these different formats in order to formulate prior distributions that align with the expert's expectations, regardless of the model structure. To address these challenges, we develop a simulation-based elicitation method that can learn the hyperparameters of potentially any parametric prior distribution from a wide spectrum of expert knowledge using stochastic gradient descent. We validate the effectiveness and robustness of our elicitation method in four representative case studies covering linear models, generalized linear models, and hierarchical models. Our results support the claim that our method is largely independent of the underlying model structure and adaptable to various elicitation techniques, including quantile-based, moment-based, and histogram-based methods.

In conversation, speakers produce language incrementally, word by word, while continuously monitoring the appropriateness of their own contribution in the dynamically unfolding context of the conversation; and this often leads them to repair their own utterance on the fly. This real-time language processing capacity is furthermore crucial to the development of fluent and natural conversational AI. In this paper, we use a previously learned Dynamic Syntax grammar and the CHILDES corpus to develop, train and evaluate a probabilistic model for incremental generation where input to the model is a purely semantic generation goal concept in Type Theory with Records (TTR). We show that the model's output exactly matches the gold candidate in 78% of cases with a ROUGE-l score of 0.86. We further do a zero-shot evaluation of the ability of the same model to generate self-repairs when the generation goal changes mid-utterance. Automatic evaluation shows that the model can generate self-repairs correctly in 85% of cases. A small human evaluation confirms the naturalness and grammaticality of the generated self-repairs. Overall, these results further highlight the generalisation power of grammar-based models and lay the foundations for more controllable, and naturally interactive conversational AI systems.